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In a question paper, there are four multiple choice type questions, each question has five choices with only one choice for it’s correct answer. What is the total number of ways in which a candidate will not get all the four answers correct?

  • A.19
  • B.120
  • C.624
  • D.1024

Answer: C

Each question has five choices, answered independently.

\[ 5^{4} = 625 \text{ ways to answer the paper} \]

Exactly one of those has all four right, so

\[ 625 - 1 = 624 \]

The complement is the whole trick: counting the ways to get at least one wrong directly would need four separate cases.

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